For motion planning, we use RRT motion planner [1]} which is probabilistically complete [2]}. Thus, given sufficient time, the probability of finding a plan, if one exists, approaches one. For the AND/OR graph network \(\Gamma = (\mathcal {G},T)\)  based task planner, by design each graph \(G^a_i\)  terminates either at a success node or a failure node and hence each \(G^a_i\)  complete. Using a predetermined depth limit \(l\) , \(\Gamma \)  is expanded at most till depth \(l\) . Thus if \(G^a_j\) , \(j\le l\)  is solved then \(\Gamma \)  is solved. Else \(\Gamma \)  is terminated at \(G^a_l\)  and a non-existence of solution is reported. In reality, a solution does not exist at all or the chosen \(l\)  is shallow. However, the first scenario (non-existence of a solution) is quashed since we are interested in TMP scenarios with solutions (consequence of our assumption). Thus, without any loss of generality, it can be argued that as \(l\)  approaches infinity the probability of \(\Gamma \)  being solved asymptotically approaches one.
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